login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A269226 Period 6: repeat [3, 9, 6, 6, 9, 3]. 1
3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The palindromic sequence arising when the digital root of n alternates diagonally in opposite directions on a square grid.  This is the sequence of 3-6-9 appearing every third column on a square grid when A010888 (digital root of n) alternates in both directions diagonally. Other columns are the digital root of 2^n: {1, 2, 4, 8, 7, 5}, or in its opposite direction 5^n: {5,7,8,4,2,1}.  All diagonals parallel to the digital roots of n are also {1,2,3,4,5,6,7,8,9} or {9,8,7,6,5,4,3,2,1}.

See the link below for a visual illustration.

This sequence also arises when A180592 (digital root of 2n) is substituted for A010888.

Decimal expansion of 40070/10101. - David A. Corneth, Jul 12 2016

LINKS

Table of n, a(n) for n=1..96.

Peter M. Chema, Illustration of initial terms

Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1).

FORMULA

a(n+1) = digital root of 5^n - 2^n.

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) = a(n-6). - Charles R Greathouse IV, Jul 12 2016

a(n) = (12 - 3*cos(n*Pi/3) - 3*cos(2*n*Pi/3) - sqrt(3)*sin(n*Pi/3) - 3*sqrt(3)*sin(2*n*Pi/3))/2. - Wesley Ivan Hurt, Oct 05 2018

PROG

(PARI) a(n)=[3, 3, 9, 6, 6, 9][n%6+1] \\ Charles R Greathouse IV, Jul 12 2016

CROSSREFS

Cf. A010888, A180592.

Sequence in context: A201614 A021720 A153416 * A205557 A193078 A021256

Adjacent sequences:  A269223 A269224 A269225 * A269227 A269228 A269229

KEYWORD

nonn,base,easy

AUTHOR

Peter M. Chema, Jul 11 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 21 17:20 EDT 2019. Contains 325198 sequences. (Running on oeis4.)